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An unconditionally stable explicit algorithm for structural dynamics
Author(s) -
Trujillo D. M.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620111008
Subject(s) - damping matrix , diagonal , stiffness , mass matrix , mathematics , stability (learning theory) , matrix (chemical analysis) , positive definite matrix , stiffness matrix , algorithm , diagonal matrix , dynamics (music) , mathematical analysis , computer science , geometry , physics , structural engineering , engineering , eigenvalues and eigenvectors , materials science , quantum mechanics , machine learning , neutrino , nuclear physics , acoustics , composite material
This paper presents an unconditionally stable explicit algorithm for the direct integration of the structural dynamic equations of motion. The algorithm is restricted to a diagonal mass matrix and positive definite symmetric stiffness and damping matrices. The algorithm is based on splitting the stiffness and damping matrices into strictly lower and upper trangular form. Unconditional stability is proven, but only for the undamped case and a completely symmetric splitting of the stiffness matrix. An alternate splitting method is also presented and numerical examples indicate superior performance over the symmetric splitting, but only a conditional stability. A spring‐mass‐dashpot model is used to illustrate the algorithm.